If each side of a square is increased by 10%, its area will be increased by :

Let the original length of sides be x
Then, new length :
$$\eqalign{ & = \left( {110\% {\text{ of }}x} \right) \cr & = \frac{{11x}}{{10}} \cr} $$
Original area $${x^2}$$
New area :
$$\eqalign{ & = {\left( {\frac{{11x}}{{10}}} \right)^2} \cr & = \frac{{121{x^2}}}{{100}} \cr} $$
Increase in area :
$$\eqalign{ & = \left( {\frac{{121{x^2}}}{{100}} - {x^2}} \right) \cr & = \frac{{21{x^2}}}{{100}} \cr} $$
∴ Increase % :
$$\eqalign{ & = \left( {\frac{{21{x^2}}}{{100}} \times \frac{1}{{{x^2}}} \times 100} \right)\% \cr & = 21\% \cr} $$